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# 1027. Longest Arithmetic Subsequence

<https://leetcode.com/problems/longest-arithmetic-subsequence>

## Description

Given an array `nums` of integers, return the **length** of the longest arithmetic subsequence in `nums`.

Recall that a *subsequence* of an array `nums` is a list `nums[i1], nums[i2], ..., nums[ik]` with `0 <= i1 < i2 < ... < ik <= nums.length - 1`, and that a sequence `seq` is *arithmetic* if `seq[i+1] - seq[i]` are all the same value (for `0 <= i < seq.length - 1`).

**Example 1:**

```
**Input:** nums = [3,6,9,12]
**Output:** 4
**Explanation:** 
The whole array is an arithmetic sequence with steps of length = 3.
```

**Example 2:**

```
**Input:** nums = [9,4,7,2,10]
**Output:** 3
**Explanation:** 
The longest arithmetic subsequence is [4,7,10].
```

**Example 3:**

```
**Input:** nums = [20,1,15,3,10,5,8]
**Output:** 4
**Explanation:** 
The longest arithmetic subsequence is [20,15,10,5].
```

**Constraints:**

* `2 <= nums.length <= 1000`
* `0 <= nums[i] <= 500`

## ac

```java
```